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- // This file is part of Eigen, a lightweight C++ template library
- // for linear algebra.
- //
- // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
- //
- // This Source Code Form is subject to the terms of the Mozilla
- // Public License v. 2.0. If a copy of the MPL was not distributed
- // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
- #ifndef EIGEN_EULERANGLES_H
- #define EIGEN_EULERANGLES_H
- namespace Eigen {
- /** \geometry_module \ingroup Geometry_Module
- *
- *
- * \returns the Euler-angles of the rotation matrix \c *this using the convention defined by the triplet (\a a0,\a a1,\a a2)
- *
- * Each of the three parameters \a a0,\a a1,\a a2 represents the respective rotation axis as an integer in {0,1,2}.
- * For instance, in:
- * \code Vector3f ea = mat.eulerAngles(2, 0, 2); \endcode
- * "2" represents the z axis and "0" the x axis, etc. The returned angles are such that
- * we have the following equality:
- * \code
- * mat == AngleAxisf(ea[0], Vector3f::UnitZ())
- * * AngleAxisf(ea[1], Vector3f::UnitX())
- * * AngleAxisf(ea[2], Vector3f::UnitZ()); \endcode
- * This corresponds to the right-multiply conventions (with right hand side frames).
- *
- * The returned angles are in the ranges [0:pi]x[-pi:pi]x[-pi:pi].
- *
- * \sa class AngleAxis
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC inline Matrix<typename MatrixBase<Derived>::Scalar,3,1>
- MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const
- {
- EIGEN_USING_STD_MATH(atan2)
- EIGEN_USING_STD_MATH(sin)
- EIGEN_USING_STD_MATH(cos)
- /* Implemented from Graphics Gems IV */
- EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived,3,3)
- Matrix<Scalar,3,1> res;
- typedef Matrix<typename Derived::Scalar,2,1> Vector2;
- const Index odd = ((a0+1)%3 == a1) ? 0 : 1;
- const Index i = a0;
- const Index j = (a0 + 1 + odd)%3;
- const Index k = (a0 + 2 - odd)%3;
-
- if (a0==a2)
- {
- res[0] = atan2(coeff(j,i), coeff(k,i));
- if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0)))
- {
- if(res[0] > Scalar(0)) {
- res[0] -= Scalar(EIGEN_PI);
- }
- else {
- res[0] += Scalar(EIGEN_PI);
- }
- Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
- res[1] = -atan2(s2, coeff(i,i));
- }
- else
- {
- Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
- res[1] = atan2(s2, coeff(i,i));
- }
-
- // With a=(0,1,0), we have i=0; j=1; k=2, and after computing the first two angles,
- // we can compute their respective rotation, and apply its inverse to M. Since the result must
- // be a rotation around x, we have:
- //
- // c2 s1.s2 c1.s2 1 0 0
- // 0 c1 -s1 * M = 0 c3 s3
- // -s2 s1.c2 c1.c2 0 -s3 c3
- //
- // Thus: m11.c1 - m21.s1 = c3 & m12.c1 - m22.s1 = s3
-
- Scalar s1 = sin(res[0]);
- Scalar c1 = cos(res[0]);
- res[2] = atan2(c1*coeff(j,k)-s1*coeff(k,k), c1*coeff(j,j) - s1 * coeff(k,j));
- }
- else
- {
- res[0] = atan2(coeff(j,k), coeff(k,k));
- Scalar c2 = Vector2(coeff(i,i), coeff(i,j)).norm();
- if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0))) {
- if(res[0] > Scalar(0)) {
- res[0] -= Scalar(EIGEN_PI);
- }
- else {
- res[0] += Scalar(EIGEN_PI);
- }
- res[1] = atan2(-coeff(i,k), -c2);
- }
- else
- res[1] = atan2(-coeff(i,k), c2);
- Scalar s1 = sin(res[0]);
- Scalar c1 = cos(res[0]);
- res[2] = atan2(s1*coeff(k,i)-c1*coeff(j,i), c1*coeff(j,j) - s1 * coeff(k,j));
- }
- if (!odd)
- res = -res;
-
- return res;
- }
- } // end namespace Eigen
- #endif // EIGEN_EULERANGLES_H
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